Simulating electron wave dynamics in graphene superlattices exploiting parallel processing advantages

This work introduces a parallel computing framework to characterize the propagation of electron waves in graphene-based nanostructures. The electron wave dynamics is modeled using both “microscopic” and effective medium formalisms and the numerical solution of the two-dimensional massless Dirac equation is determined using a Finite-Difference Time-Domain scheme. The propagation of electron waves in graphene superlattices with localized scattering centers is studied, and the role of the symmetry of the microscopic potential in the electron velocity is discussed. The computational methodologies target the parallel capabilities of heterogeneous multi-core CPU and multi-GPU environments and are built with the OpenCL parallel programming framework which provides a portable, vendor agnostic and high throughput-performance solution. The proposed heterogeneous multi-GPU implementation achieves speedup ratios up to 75x when compared to multi-thread and multi-core CPU execution, reducing simulation times from several hours to a couple of minutes.本研究提出一款并行计算框架，用于表征石墨烯基纳米结构中电子波的传播特性。研究采用“微观”与有效介质两种形式化方法对电子波动力学进行建模，并采用时域有限差分（Finite-Difference Time-Domain）方法求解二维无质量狄拉克方程的数值解。针对带有局域散射中心的石墨烯超晶格内的电子波传播行为展开研究，探讨了微观势场对称性对电子速度的影响。本计算方法针对异构多核CPU与多图形处理器（GPU）环境的并行特性开发，基于开放计算语言（OpenCL）并行编程框架构建，该框架可提供可移植、厂商无关且高吞吐性能的解决方案。所提出的异构多GPU实现相较于多线程与多核CPU执行，可实现最高75倍的加速比，将仿真时长从数小时缩短至数分钟。